Right from the Slate article that Piezoe posted, there's a good example:
Sure, you can go online and see every asset on the Fed’s balance sheet, including its serial tracking number. But, Paul says, that doesn’t tell readers “who they bought them from or whether they were bought at fair market price or whether they were bought at a haircut and whether or not there were any conflicts of interests in the buying and selling.”
Additionally, I'd like to know why the Fed fought so hard and for so long to release the names of banks that borrowed from the discount window during the crisis, and why - when they finally were ordered by the court to turn over the info - they still held back information.
Further, I'd like to know why the Fed continues to ignore investigations into leaks of information, and why anyone who asks a question on it (like good ol' Pedro) gets dismissed.
These are just some examples. It's a shadowy organization that hides information under the pretense that "it's fully transparent and everything is there for you to see" yet fights tooth and nail to keep things hidden on request. If there were nothing to hide, why all the fighting to do so?
To pretend that the Fed is independent in it's monetary policy setting is downright hilarious. Banks "advise" the Fed what to do, and it does it. End of story. The Fed has never (that I can recall) done something against the bank's "recommendation". Perhaps back in Volcker's day.